In simple words it is the probability outcome changes given another event occurring.
You can find it in this form P (A | B), that means the probability of the event A occurring given the event B
Image source : Xie, S. (n.d.). Conditional Probability - Statistical Guess. Medium. https://medium.com/statistical-guess/conditional-probability-1114ae169f49
- The probability of having a 3 taking into account that the result of a dice roll is an odd value.
- The probability of getting 3 on a 6 faced dice is 1/6.
- A 6 sided die can only have 3 odd values 1,3 and 5.
- P (A | B) would be equal to P (A ∩ B) / P (B) = (1/6)/(1/2) = 1/6 *2/1 = 1/3.
- So, taking into account an odd result when rolling the dice, we have 1/3 probability to get a 5.
- In Algeria we recently attended national exams among these exams the "BAC" we will use this event to explain the conditional probabilities.
- We will take a sample of 100 men and 100 women and compare the results obtained (passed the exam and did not pass the exam).
- The women who passed the exam are 92 out of 200, compared to the number of all the people who passed the exam which is 169 out of 200.
- P (A | B) = (92/200)/(169/200).
- P (A | B) = 0.54 So if I randomly take one person among who passed the exam, 54% chance that the person is a woman.
